Quantifying incompatibility of quantum measurements through non-commutativity

• URL: http://arxiv.org/abs/2110.10646v2
• Date: Mon, 22 Nov 2021 11:38:15 GMT
• Title: Quantifying incompatibility of quantum measurements through non-commutativity
• Authors: Krzysztof Mordasewicz, J\k{e}drzej Kaniewski
• Abstract summary: Incompatible measurements are an important distinction between quantum mechanics and classical theories. We explore a family of incompatibility measures based on non-commutativity. We show that they satisfy some natural information-processing requirements. We also consider the behavior of our measures under different types of compositions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While incompatibility might at first glance seem like an obstacle, it turns to be a necessary ingredient to achieve the so-called quantum advantage in various operational tasks like random access codes or key distribution. To improve our understanding of how to quantify incompatibility of quantum measurements, we define and explore a family of incompatibility measures based on non-commutativity. We investigate some basic properties of these measures, we show that they satisfy some natural information-processing requirements and we fully characterize the pairs which achieve the highest incompatibility (in a fixed dimension). We also consider the behavior of our measures under different types of compositions. Finally, to link our new measures to existing results, we relate them to a robustness-based incompatibility measure and two operational scenarios: random access codes and entropic uncertainty relations.

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